Some Observations on Pm,n Relations within Set Classes
Identifieur interne : 000371 ( Main/Merge ); précédent : 000370; suivant : 000372Some Observations on Pm,n Relations within Set Classes
Auteurs : Michael RussSource :
- Music Analysis [ 0262-5245 ] ; 2007-03.
English descriptors
- Teeft :
- Adjacent integers, Atonal, Blackwell, Blackwell publishing, Boris godunov, Callender, Cardinality, Chorale, Chord, Class comments, Cohn, Cohn functions, Contrary motion, David lewin, Diatonic, Different ways, Diminution, Dominant sevenths, Douth2, Douthett, Dyad, Easy piano pieces, Form relations, Generalized chord spaces, Harmonic, Hexachord, Hexachords, Hungarian peasant songs, Interval, Interval class, Interval string, Interval strings, Interval vectors, Invariant subset, Invariant subsets, Invariant tetrachord, Invariant tetrachords, Invariant trichord, Inversion, Italic, Journal compilation, Large number, Larger cardinality, Lewin, Major scale, Maximally, Michael russ, Minor triad, More relations, Music analysis, Music theory, Musorgsky, Mystic chord, Octatonic, Parsimonious, Parsimony, Pentachordal, Pentachords, Perturbation, Pitch class, Pitch classes, Power towers, Prime form, Prime forms, Progression, Relation results, Retrograde rotation, Richard cohn, Right hand, Rus, Same class, Same time, Scriabin, Semitonal, Semitone, Seventh chords, Similar motion, Single relation, Single semitonal perturbation, Small number, Subset, Such relations, Tetrachord, Tetrachordal, Tetrachords, Tonality, Transposition, Triad, Trichord, Trichords, Tymoczko, Voices move, Whole step, Whole tone, Whole tones, Wind instruments.
Abstract
It is well known (from Riemann, Lewin, Cohn and others) that two voices of a triad (set class 3–11) may be held and one moved ‘parsimoniously’ by a tone or semitone to produce another triad; or two voices of a dominant and half‐diminished seventh (set class 4–27) may be held while two voices are displaced by a semitone to produce another dominant or half‐diminished seventh (Lewin's ‘DOUTH2’ relation). This article takes 4–27 as its starting point and first explores examples of such parsimonious voice‐leading between sets of the same class in nineteenth‐century music (notably Brahms, Chopin and Musorgsky). The discussion introduces the idea of a diminution existing between forms of 4–27 when the two voices do not proceed simultaneously. The capability of tetrachords of other classes as well as set classes of larger cardinality to engage in parsimonious voice‐leading either by semitone or whole tone is then explored (with examples drawn from the music of Bartók, Mahler, Scriabin and Stravinsky). The type and degree of parsimony are indicated by the Pm,n designations developed by Douthett and Steinbach, and the article examines the ways in which the capacity of sets to behave in this manner may be predicted from interval strings and invariant subsets.
Url:
DOI: 10.1111/j.1468-2249.2007.00251.x
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<term>Hungarian peasant songs</term>
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<term>Perturbation</term>
<term>Pitch class</term>
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<term>Power towers</term>
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<term>Trichords</term>
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<front><div type="abstract" xml:lang="en">It is well known (from Riemann, Lewin, Cohn and others) that two voices of a triad (set class 3–11) may be held and one moved ‘parsimoniously’ by a tone or semitone to produce another triad; or two voices of a dominant and half‐diminished seventh (set class 4–27) may be held while two voices are displaced by a semitone to produce another dominant or half‐diminished seventh (Lewin's ‘DOUTH2’ relation). This article takes 4–27 as its starting point and first explores examples of such parsimonious voice‐leading between sets of the same class in nineteenth‐century music (notably Brahms, Chopin and Musorgsky). The discussion introduces the idea of a diminution existing between forms of 4–27 when the two voices do not proceed simultaneously. The capability of tetrachords of other classes as well as set classes of larger cardinality to engage in parsimonious voice‐leading either by semitone or whole tone is then explored (with examples drawn from the music of Bartók, Mahler, Scriabin and Stravinsky). The type and degree of parsimony are indicated by the Pm,n designations developed by Douthett and Steinbach, and the article examines the ways in which the capacity of sets to behave in this manner may be predicted from interval strings and invariant subsets.</div>
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